Sir Roger Penrose, one of the world’s leading experts on the science of consciousness, delivered a lecture entitled “Science and the Mind” on Friday, Oct. 12 in Chapin Hall.
Penrose, who holds professorships at Oxford University, Gresham College in London, and Penn State University, was knighted in 1994 “for service to science.” His numerous awards include the 1989 Wolf Prize, which he shared with the world-renowned theoretical physicist Stephen Hawking.
Drawing on findings and principles from mathematics, physics, philosophy and neuroscience, Penrose argued that machines will never be able to imitate human consciousness.
He opened the lecture by asking “whether consciousness can be understood with computation, with existing science, with an extended physical worldview or with something beyond science.”
“I want to argue for the third possibility,” Penrose said. “Our present-day science is not broad enough to understand mentality. I do believe, however, that [we need] science of some kind, and not something beyond science.”
Penrose proposed that there are three “worlds,” each of which is connected to the other two in some way: a Platonic world of mathematical absolutes, a physical world and a mental world. Since not all of mathematics is accessible by computation, he argued, there may be aspects of the physical world that cannot be reduced to mechanical rules, and these areas may be responsible for the functioning of the mind.
Penrose made the case for this assertion with several mathematical examples.
One example was Goodstein’s theorem, which involves sequences of exponential numbers that appear to grow increasingly large but in fact eventually reduce to zero.
While the theorem uses simple arithmetic rules, it cannot be proven by ordinary induction.
Penrose noted that Goodstein’s theorem is a specific instance of the more general GÃ¶del’s theorem, which demonstrates the existence of mathematical statements that are dependent on a set of rules but cannot be explained with those rules alone.
Penrose also presented a simple formula for a tiling, a series of interlocking and non-overlapping two-dimensional shapes that never repeats itself but covers all points in an infinitely large plane. “The evolution of the tiles is deterministic but non-computable,” Penrose explained. “It is quite conceivable that there are physical laws outside of computation.”
Penrose then proposed that these hypothetical non-computable laws exist in the “magnification process” between classical physics and quantum mechanics.
He noted that quantum mechanics can only reveal the probabilities that certain outcomes will happen, while observable physical events either happen or do not happen. The gap between the two levels is known as the problem of measurement.
A famous formulation of this question is the problem of SchrÃ¶dinger’s cat. Erwin SchrÃ¶dinger, who authored the central equation of quantum physics that bears his name, devised a hypothetical situation in which his cat would either be shot or not shot depending on the outcome of a quantum event.
“SchrÃ¶dinger was troubled by his own equation,” Penrose said. “[Taken literally], it would require his cat being dead and alive at the same time.”
Penrose expressed his belief that we need “something we don’t know yet” to solve the problems like that of SchrÃ¶dinger cat, which are known as “quantum superpositions.” For Penrose and a minority of physicists, the missing link is what is known as an “objective reduction,” a physical process that “decides” between quantum possibilities. According to Penrose, the objective reduction could show the non-computability that he referred to earlier.
In concluding the lecture Penrose proposed that the neuronal events responsible for consciousness may fall in the realm of the “borderline physics” between classical physics and quantum theory. He noted that the microtubules (elements of a cellular “skeleton”) in neurons are believed by some scientists to be involved in consciousness, and that different conformational states of microtubule proteins may exhibit quantum effects.
If these assumptions are true, the non-computational aspects of neuron function could then lie in the effects of these protein conformations on neuronal behavior.
William Wootters, a professor of physics who specializes in quantum information, said, “Roger Penrose has made tremendous contributions to physics, especially to general relativity, and it was great to have him here at Williams.”
“Although my own views on the nature of the mind are not the same as his,” he continued, “I agree with him that consciousness is deeply mysterious and I respect him for trying to make sense of it. I also agree that the problem of consciousness is related to what is called the ‘problem of measurement’ in quantum physics.”
“I thought Sir Penrose was amazing,” said Leon Webster ’04. “I had never questioned the ability of a computer to emulate consciousness given enough processing power and memory, but his example of a deterministic but noncomputable system is intriguing, and the implication that human consciousness might be another such system calls into question my entire paradigm on the mind.”
The lecture committee, the Dean of the Faculty, and the departments of astronomy, mathematics, computer science and physics sponsored the lecture.